Open Source means that most of the programming of the operating system is accessible to people who make apps. This is why you can get apps to replace the onscreen keyboard or music player. This can't be done on the iPhone and many other smartphones.

Another example is Google Voice which lets you make calls and text via GV instead of your normal number. Apple didn't like this and removed it from the AppStore. Android lets you put out any app that isn't malicious as far as I know.

Even things like downloading files. On Android you can download zip files, pdf files, text files, whatever and save them to your SD card. Don't even think about this on an iPhone or even many other smartphones that only allow you to download pictures or certain other formats.

It just gives more freedom to the user and app-makers to do what they want to do.

Edit: So basically, the answer is. As an end user, you will see more apps available to do more things. If you need something done there is probably an app to do it or someone who can make an app to do it.